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Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation

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Hiroaki Kusunose

Strongly Correlated Electrons · Submitted 20 Feb 2006 · 57 references

Pith's reading: An IPT-based local susceptibility is used to add nonlocal antiferromagnetic fluctuations to the DMFT self-energy, yielding a pseudogap and enhanced specific heat in the half-filled 2D Hubbard model.

T0 · AI review

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arXiv IDcond-mat/0602451 (version 2)
Pith IDIDPE7A2L, Pith's permanent record of this paper and its review
CitationHiroaki Kusunose. "Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation." arXiv:cond-mat/0602451 (2006). https://pith.science/paper/IDPE7A2L
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Claim paper
The paper

The paper claims

An IPT-based local susceptibility is used to add nonlocal antiferromagnetic fluctuations to the DMFT self-energy, yielding a pseudogap and enhanced specific heat in the half-filled 2D Hubbard model.

The reading

The Hubbard model describes electrons hopping on a lattice that repel each other when two occupy the same site. In two dimensions, this model is a standard test bed for theories of strongly correlated materials, including the cuprate superconductors. A powerful tool, dynamical mean field theory (DMFT), treats each site as an impurity embedded in a bath and captures local physics exactly in infinite dimensions, but it misses spatial correlations. This paper extends DMFT by adding back the effect of spin fluctuations between different lattice sites.

The author first solves the DMFT equations using iterated perturbation theory (IPT), a fast approximate impurity solver. From that solution he extracts a local but energy-dependent two-particle vertex and builds the momentum-dependent spin susceptibility through a Bethe-Salpeter equation. The nonlocal part of this susceptibility is then fed back into the self-energy as a one-shot correction. At half-filling and moderate interaction strength, the correction is small at high temperature but grows as the temperature approaches the antiferromagnetic instability, where the staggered susceptibility diverges. As a result, the central quasiparticle peak in the density of states splits, producing a pseudogap, and the double occupancy drops, indicating stronger Mott localization. The specific heat is also enhanced near the transition.

The approach is approximate and the author lists its limitations: the spectral function of the constructed susceptibility is slightly negative at high energy, the spin susceptibility fails the local moment sum rule, and the self-energy is not updated self-consistently. The paper nevertheless shows a concrete route to include nonlocal correlations on top of DMFT without a full cluster calculation.

Extended reading notes

Core claim

The abstract states: "It is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation." If correct, the paper shows that nonlocal spin fluctuations added on top of a DMFT local self-energy produce a pseudogap and enhance the specific heat through reduced double occupancy.

Load-bearing premise

The load-bearing approximation is eq. (2.6): the irreducible two-particle vertices are taken to depend only on the external bosonic energy, Gamma_alpha(k,k';q) ~ Gamma_alpha(epsilon_m). This neglects all momentum and fermionic frequency structure in the vertex. The paper itself states in Sec. 3.2 that the source of the discrepancy in the Neel temperature comes from this simplification of the spin vertex rather than from the IPT approximation itself. If realistic vertex structure is required, the constructed nonlocal susceptibility, and therefore the pseudogap, could change.

Original abstract

We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. We briefly discuss a formulation for the superconducting transition temperature in the present approximation.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,304 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. We briefly discuss a formulation for the superconducting transition temperature in the present approximation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. contribution 0.96 0.91 0.09 asserted 0.91
s1 For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. method 0.92 0.86 0.04 asserted 0.95
s2 Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. result 1.00 0.93 0.61 asserted 1.00
s3 The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. result 0.96 0.87 0.13 asserted 1.00
s4 We briefly discuss a formulation for the superconducting transition temperature in the present approximation. future work 0.64 0.73 0.03 unclear 0.81

What kind of paper the classifier reports this is: method or tool 0.95 · evidence from simulation or computation 0.80.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. The Feynman diagrams for (a) the Bethe-Salpeter equa
Figure 2. The T dependence of the static local spin susceptibility for U = 8, 10 and 16. The dotted line represents the Curie law in the atomic limit. with Uch, we can compute the approximate local spin suscep￾tibility within the IPT scheme. The charge vertex Uch is turned out to be rapidly increase function of U, and hence the charge susceptibility is negligible in strong U region. 3.2 Validity of approximate spin susceptibility Let us examine the validity of the approximate spin suscep￾tibility as follows. We have used the tight-binding DOS, ρ0(ǫ), of the two-dimensional square lattice with…
Figure 4. The spectral intensity of the local spin susceptibil
Figure 7. The U-T phase diagram for half-filling. Tc1 and Tc2 are the metal￾insulator transition temperatures determined by DMFT. Tcoh is the coher￾ent temperature, below which the coherent state develops near the chemical potential. The N´eel temperature TN is determined by eq. (2.7b)
Figure 8. The contour plot of the spectral intensity
Figure 9. The density of states for U = 8. (a) temperature dependences, (b) comparison with the DMFT results. the Brillouin zone. The overall structure of the spectral in￾tensity is roughly the same as that obtained by eq. (2.4) with the DMFT self-energy (not shown). In contrast to the DMFT intensity, the pseudo-gap behaviors at ω = 0 appears in the coherent quasiparticle state due to the strong AF spin fluctu￾ation (see, the X-M’ line).35–41 Note that there exist the hot spots over the entire Fermi surface, since the magnetic Bril￾louin zone coincides with the Fermi surface. The pseudo-gap…
Figure 11. The T dependences of the specific heat for U = 8. The inset shows the T dependence of the double occupancy. The results of DMFT is shown for comparison. using the 6 × 6 square lattice shows the T dependence of the specific heat similar to that of the DMFT.44 This implies the importance of the long-range critical fluctuations. 5. Summary and Discussion We have proposed the formulation to take into account the correction of the spatial correlations to the local self-energy obtained by DMFT. It is demonstrated that the one-particle spectral intensity of the 2D Hubbard model at half-fil

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References
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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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